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Theorem dfpss3 3024
Description: Alternate definition of proper subclass. (Contributed by NM, 7-Feb-1996.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
dfpss3  C.  C_  C_

Proof of Theorem dfpss3
StepHypRef Expression
1 dfpss2 3023 . 2  C.  C_
2 eqss 2954 . . . . 5 
C_  C_
32baib 827 . . . 4 
C_  C_
43notbid 591 . . 3 
C_  C_
54pm5.32i 427 . 2  C_  C_  C_
61, 5bitri 173 1  C.  C_  C_
Colors of variables: wff set class
Syntax hints:   wn 3   wa 97   wb 98   wceq 1242    C_ wss 2911    C. wpss 2912
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-ne 2203  df-in 2918  df-ss 2925  df-pss 2927
This theorem is referenced by:  pssirr  3038  pssn2lp  3039  ssnpss  3041  nsspssun  3164  npss0  3260
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